Finite Group Databasebeta

← C2×#20246327 #26375616

Subgroups — C2×#20246327 #26375616

Order 12032.

3374 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093986C211yesmaximal, characteristic
2#20246327C2116yesmaximal, direct product factor
3C2×#15689015C211yesmaximal, characteristic, complemented
4C2×#15689013C211yesmaximal, characteristic, complemented
5C2×#15689009C211yesmaximal, characteristic, complemented
6C2×#15689001C211yesmaximal, characteristic
7C2×#15689001C211yesmaximal, characteristic
8C2×#15688990C211yesmaximal, characteristic, complemented
9C2×#15688985C211yesmaximal, characteristic, complemented
10C2×#15688980C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
13C2×#15688970C211yesmaximal, characteristic, complemented
14C2×#15688968C211yesmaximal, characteristic, complemented
15C2×#95×D47C211yesmaximal, characteristic, complemented
16C2×C47×#387C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C2×#13093986C4116yescomplemented
23C2×#13093986C2218yes—
24C22×C4⋊Dic47C2211yescharacteristic
25C22×(C2×D47)⋊C4C2211yescharacteristic
26C22×(C2×D47)⋊C4C2211yescharacteristic
27C22×(C2×D47)⋊C4C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37#15689015C2218yescomplemented
38#15689013C2218yescomplemented
39#15689009C2218yescomplemented
40#15689001C2218yes—
41#15689001C2218yes—
42#15688990C2218yescomplemented
43#15688985C2218yescomplemented
44#15688980C2218yescomplemented
45C4×(C2×D47)⋊C4C2218yescomplemented
46C4×(C2×D47)⋊C4C2218yescomplemented
47#15688970C2218yescomplemented
48#15688968C2218yescomplemented
49C2×C47⋊#95C2211yescharacteristic
50C2×C47⋊#95C2211yescharacteristic
51C2×C47⋊#95C2211yescharacteristic
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59#95×D47C2218yescomplemented
60C22×C4⋊C4×C47C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C42×C47C2211yescharacteristic
63C47×#387C2218yescomplemented
64C2×#95×C47C2211yescharacteristic
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C24×D47C2311yescharacteristic
69C24×D47C2311yescharacteristic
70C22×D188—24no—
71C22×D188—24no—
72C22×D188C2×C418yes—
73C22×D188C2314yes—
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C22×C4×D47—24no—
81C22×C4×D47—24no—
82C22×C4×D47—24no—
83C22×C4×D47—24no—
84C22×C4×D47—42no—
85C22×C4×D47—42no—
86C22×C4×D47—42no—
87C22×C4×D47—42no—
88C22×C4×D47—42no—
89C22×C4×D47—42no—
90C22×C4×D47C2×C418yes—
91C22×C4×D47C2×C418yescomplemented
92C22×C4×D47C2314yes—
93C22×C4×D47C2314yes—
94C22×C4×D47C2314yes—
95C22×C4×D47C2314yes—
96#13093986C2×C4164yescomplemented
97C2×C4⋊Dic47—42no—
98C2×C4⋊Dic47C2314yes—
99C2×(C2×D47)⋊C4—24no—
100C2×(C2×D47)⋊C4—24no—
101C2×(C2×D47)⋊C4—24no—
102C2×(C2×D47)⋊C4—24no—
103C2×(C2×D47)⋊C4—42no—
104C2×(C2×D47)⋊C4—42no—
105C2×(C2×D47)⋊C4C2×C418yes—
106C2×(C2×D47)⋊C4C2×C418yescomplemented
107C2×(C2×D47)⋊C4C2314yes—
108C2×(C2×D47)⋊C4C2314yes—
109C2×(C2×D47)⋊C4C2314yes—
110C2×(C2×D47)⋊C4C2314yes—
111C2×(C2×D47)⋊C4C2314yes—
112C2×(C2×D47)⋊C4C2314yes—
113C2×(C2×D47)⋊C4C2314yes—
114C2×(C2×D47)⋊C4C2314yes—
115C2×C4×Dic47—24no—
116C2×C4×Dic47—24no—
117C2×C4×Dic47—42no—
118C2×C4×Dic47C2×C418yescomplemented
119C2×C4×Dic47C2314yes—
120C2×C4×Dic47C2314yes—
121C2×C4×Dic47C2314yes—
122C2×C4×Dic47C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47—42no—
141C2×C4⋊C4×C47C2×C418yescomplemented
142C2×C4⋊C4×C47C2314yes—
143C2×C4⋊C4×C47C2314yes—
144C2×C42×C47—42no—
145C2×C42×C47C2314yes—
146#95×C47C2314yes—
147#95×C47C2314yes—
148#95×C47C2314yes—
149#95×C47C2314yes—
150C24×C47C2411yescharacteristic
151C23×D47—22no—
152C23×D47—22no—
153C23×D47—22no—
154C23×D47—22no—
155C23×D47—22no—
156C23×D47—22no—
157C23×D47—22no—
158C23×D47—22no—
159C23×D47—22no—
160C23×D47—22no—
161C23×D47C22×C414yes—
162C23×D47C22×C414yes—
163C23×D47#4114yes—
164C23×D47#4114yes—
165C23×D47C2412yes—
166C23×D47C2412yes—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47C22×C414yes—
185C22×C4×C47C22×C414yes—
186C22×C4×C47C22×C414yes—
187C22×C4×C47#4114yes—
188C22×C4×C47C2412yes—
189C22×C4×C47C2412yes—
190C22×C4×C47C2412yes—
191C22×C4×C47C2412yes—
192C22×C4×C47C2412yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47C22×C414yes—
211C22×Dic47C22×C414yes—
212C22×Dic47#4114yes—
213C22×Dic47C2412yes—
214C22×Dic47C2412yes—
215C22×Dic47C2412yes—
216C22×Dic47C2412yes—
217C22×Dic47C2412yes—
218C22×Dic47C2412yes—
219C2×D188—232no—
220C2×D188—28no—
221C2×D188—28no—
222C2×D188C22×C4116yes—
223C2×C4×D47—28no—
224C2×C4×D47—28no—
225C2×C4×D47—28no—
226C2×C4×D47—28no—
227C2×C4×D47—416no—
228C2×C4×D47—416no—
229C2×C4×D47—44no—
230C2×C4×D47—44no—
231C2×C4×D47—44no—
232C2×C4×D47—44no—
233C2×C4×D47—44no—
234C2×C4×D47—44no—
235C2×C4×D47—416no—
236C2×C4×D47—416no—
237C2×C4×D47C22×C4116yes—
238C2×C4×D47C22×C4116yescomplemented
239C4⋊C4×C47—44no—
240C4⋊C4×C47C22×C4116yescomplemented
241C42×C47—44no—
242(C2×D47)⋊C4—28no—
243(C2×D47)⋊C4—28no—
244(C2×D47)⋊C4—28no—
245(C2×D47)⋊C4—28no—
246(C2×D47)⋊C4—44no—
247(C2×D47)⋊C4—44no—
248(C2×D47)⋊C4C22×C4116yes—
249(C2×D47)⋊C4C22×C4116yescomplemented
250C4⋊Dic47—44no—
251C4×Dic47—28no—
252C4×Dic47—28no—
253C4×Dic47—44no—
254C4×Dic47C22×C4116yescomplemented
255C23×C47C23×C412yes—
256C23×C47C2×#4112yes—
257C23×C47C2×#4112yes—
258C23×C47C2×#4112yes—
259C23×C47C2×#4112yes—
260C23×C47H(5,𝔽2)12yes—
261C23×C47H(5,𝔽2)12yes—
262C23×C47C2511yescharacteristic
263C22×D47—28no—
264C22×D47—28no—
265C22×D47—28no—
266C22×D47—28no—
267C22×D47—28no—
268C22×D47—28no—
269C22×D47—22no—
270C22×D47—22no—
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—28no—
274C22×D47—28no—
275C22×D47—28no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—44no—
283C22×D47—44no—
284C22×D47—44no—
285C22×D47—44no—
286C22×D47#117116yes—
287C22×D47C23×C414yes—
288C22×D47C23×C414yes—
289C22×D47C2×#4114yes—
290C22×D47C2×#4114yes—
291C2×C4×C47—28no—
292C2×C4×C47—28no—
293C2×C4×C47—28no—
294C2×C4×C47—28no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—44no—
313C2×C4×C47—44no—
314C2×C4×C47—44no—
315C2×C4×C47C23×C414yes—
316C2×C4×C47C23×C414yes—
317C2×C4×C47C23×C414yes—
318C2×C4×C47C2×#4114yes—
319C2×Dic47—28no—
320C2×Dic47—28no—
321C2×Dic47—28no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—44no—
338C2×Dic47—44no—
339C2×Dic47—44no—
340C2×Dic47C23×C414yes—
341C2×Dic47C23×C414yes—
342C2×Dic47C2×#4114yes—
343D188—232no—
344C4×D47—416no—
345C4×D47—416no—
346C4×D47—416no—
347C4×D47—416no—
348C2×#2353—471nomaximal, Sylow
349C22×C47C2×#11714yes—
350C22×C47C4×#4114yes—
351C22×C47#51814yes—
352C22×C47#55114yes—
353C22×C47#55114yes—
354C22×C47#55314yes—
355C22×C47#55314yes—
356C22×C47C24×C411yescharacteristic
357C22×C47C22×#4111yescharacteristic
358C22×C47C22×#4111yescharacteristic
359C22×C47C22×#4111yescharacteristic
360C22×C47C22×#4111yescharacteristic
361C22×C47C2×H(5,𝔽2)11yescharacteristic
362C22×C47C2×H(5,𝔽2)11yescharacteristic
363C2×D47—232no—
364C2×D47—24no—
365C2×D47—24no—
366C2×D47—24no—
367C2×D47—24no—
368C2×D47—24no—
369C2×D47—24no—
370C2×D47—24no—
371C2×D47—24no—
372C2×D47—24no—
373C2×D47—416no—
374C2×D47—42no—
375C2×D47—42no—
376C2×D47—42no—
377C2×D47—42no—
378C2×D47C2×#11718yes—
379C4×C47—24no—
380C4×C47—24no—
381C4×C47—24no—
382C4×C47—24no—
383C4×C47—42no—
384C4×C47—42no—
385C4×C47—42no—
386Dic47—24no—
387Dic47—24no—
388Dic47—24no—
389Dic47—42no—
390Dic47—42no—
391Dic47—42no—
392C22×C4×D4—471no—
393#2353—4716no—
394C2×#388—471no—
395C2×#388—471no—
396C2×#387—471no—
397C2×#387D4711yescharacteristic, complemented
398C2×#386—471no—
399C2×#386—471no—
400C2×#383—471no—
401C2×#381—471no—
402C2×#380—471no—
403C2×C4×C22⋊C4—471no—
404C2×C4×C22⋊C4—471no—
405C2×C4×C22⋊C4—471no—
406C2×#376—471no—
407C22×#95—471no—
408C2×C47#235318yescomplemented
409C2×C47C22×#11711yescharacteristic
410C2×C47C2×C4×#4111yescharacteristic
411C2×C47C2×#51811yescharacteristic
412C2×C47C2×#55111yescharacteristic
413C2×C47C2×#55111yescharacteristic
414C2×C47C2×#55311yescharacteristic
415C2×C47C2×#55311yescharacteristic
416D47—28no—
417D47—44no—
418C23×D4—471no—
419C24×C4—471no—
420C24×C4—471no—
421C24×C4—471no—
422C24×C4—471no—
423C2×C4×D4—4716no—
424C2×C4×D4—478no—
425C22×C4⋊C4—471no—
426C22×C4⋊C4C2×D4711yescharacteristic
427C22×C4⋊C4C2×D4711yescharacteristic
428C22×C22⋊C4—471no—
429C22×C22⋊C4—471no—
430C22×C22⋊C4—471no—
431C22×C22⋊C4—471no—
432C22×C22⋊C4—471no—
433C22×C22⋊C4—471no—
434C22×C22⋊C4—471no—
435C22×C22⋊C4—471no—
436C22×C42—471no—
437C22×C42—471no—
438C22×C42—471no—
439C22×C42—471no—
440C22×C42C2×D4711yescharacteristic
441#388—478no—
442#388—478no—
443#387—478no—
444#387C2×D4718yescomplemented
445#386—478no—
446#386—478no—
447#383—478no—
448#381—478no—
449#380—478no—
450C4×C22⋊C4—478no—
451C4×C22⋊C4—478no—
452C4×C22⋊C4—478no—
453#376—478no—
454C2×#95—471no—
455C2×#95—471no—
456C2×#95—471no—
457C2×#95—471no—
458C2×#95—471no—
459C2×#95—471no—
460C2×#95—471no—
461C2×#95—471no—
462C2×#95—471no—
463C2×#95—471no—
464C2×#95—478no—
465C2×#95C2×D4711yescharacteristic
466C2×#95C2×D4711yescharacteristic
467C2×#95C2×D4711yescharacteristic
468C2×#95C2×D4711yescharacteristic
469C47C2×#235311yescharacteristic, complemented, Sylow
470C25—471no—
471C25—471no—
472C22×D4—478no—
473C22×D4—474no—
474C22×D4—944no—
475C22×D4—944no—
476C23×C4—471no—
477C23×C4—471no—
478C23×C4—471no—
479C23×C4—478no—
480C23×C4—478no—
481C23×C4—474no—
482C23×C4—474no—
483C23×C4—471no—
484C23×C4—471no—
485C23×C4—471no—
486C23×C4—474no—
487C23×C4—474no—
488C23×C4—944no—
489C23×C4—944no—
490C23×C4—944no—
491C23×C4—944no—
492C23×C4—1882no—
493C23×C4—1882no—
494C23×C4—1882no—
495C23×C4—1882no—
496C23×C4—1882no—
497C23×C4—1882no—
498C23×C4C22×D4711yescharacteristic
499C23×C4C22×D4711yescharacteristic
500C23×C4C22×D4711yescharacteristic
501C23×C4C22×D4711yescharacteristic
502C23×C4C22×D4711yescharacteristic
503C23×C4C22×D4711yescharacteristic
504C23×C4C22×D4711yescharacteristic
505C4×D4—4764no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—474no—
508C2×C4⋊C4—1882no—
509C2×C4⋊C4C4×D4718yescomplemented
510C2×C4⋊C4C22×D4714yes—
511C2×C4⋊C4C22×D4714yes—
512C2×C22⋊C4—478no—
513C2×C22⋊C4—478no—
514C2×C22⋊C4—474no—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—474no—
517C2×C22⋊C4—474no—
518C2×C22⋊C4—474no—
519C2×C22⋊C4—474no—
520C2×C22⋊C4—474no—
521C2×C22⋊C4—474no—
522C2×C22⋊C4—944no—
523C2×C22⋊C4—944no—
524C2×C22⋊C4—944no—
525C2×C22⋊C4—944no—
526C2×C22⋊C4—1882no—
527C2×C22⋊C4—1882no—
528C2×C42—42no—
529C2×C42—478no—
530C2×C42—474no—
531C2×C42—474no—
532C2×C42—474no—
533C2×C42—474no—
534C2×C42—944no—
535C2×C42—944no—
536C2×C42—1882no—
537C2×C42C22×D4714yes—
538#95—474no—
539#95—474no—
540#95—474no—
541#95—474no—
542#95—474no—
543#95—474no—
544#95—474no—
545#95—474no—
546#95—474no—
547#95—474no—
548#95C22×D4714yes—
549#95C22×D4714yes—
550#95C22×D4714yes—
551#95C22×D4714yes—
552C24—474no—
553C24—474no—
554C24—474no—
555C24—472no—
556C24—474no—
557C24—472no—
558C24—942no—
559C24—942no—
560C24—942no—
561C24—942no—
562C24—942no—
563C24—942no—
564C24—942no—
565C24—942no—
566C24—942no—
567C24—942no—
568C24C23×D4711yescharacteristic
569C2×D4—4716no—
570C2×D4—9432no—
571C2×D4—948no—
572C2×D4—948no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—474no—
591C22×C4—474no—
592C22×C4—474no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—472no—
596C22×C4—4716no—
597C22×C4—4716no—
598C22×C4—472no—
599C22×C4—472no—
600C22×C4—472no—
601C22×C4—948no—
602C22×C4—948no—
603C22×C4—948no—
604C22×C4—942no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—948no—
620C22×C4—18816no—
621C22×C4—18816no—
622C22×C4—1884no—
623C22×C4—1884no—
624C22×C4—1884no—
625C22×C4—1884no—
626C22×C4—1884no—
627C22×C4—1884no—
628C22×C4—18816no—
629C22×C4—18816no—
630C22×C4C2×C4×D4714yes—
631C22×C4C2×C4×D4714yes—
632C22×C4C2×C4×D4714yes—
633C22×C4#1062535414yes—
634C22×C4C23×D4712yes—
635C22×C4C23×D4712yes—
636C22×C4C23×D4712yes—
637C22×C4C23×D4712yes—
638C22×C4C23×D4712yes—
639C22×C4C23×D4712yes—
640C22×C4C23×D4712yes—
641C4⋊C4—44no—
642C4⋊C4—1884no—
643C4⋊C4C2×C4×D47116yescomplemented
644C22⋊C4—4716no—
645C22⋊C4—4716no—
646C22⋊C4—948no—
647C22⋊C4—948no—
648C22⋊C4—948no—
649C22⋊C4—948no—
650C22⋊C4—1884no—
651C22⋊C4—1884no—
652C42—44no—
653C42—4716no—
654C42—948no—
655C42—948no—
656C42—1884no—
657C23—4716no—
658C23—474no—
659C23—474no—
660C23—474no—
661C23—474no—
662C23—948no—
663C23—948no—
664C23—948no—
665C23—948no—
666C23—948no—
667C23—948no—
668C23—942no—
669C23—942no—
670C23—942no—
671C23—942no—
672C23—948no—
673C23—948no—
674C23—948no—
675C23—942no—
676C23—942no—
677C23—942no—
678C23—942no—
679C23—942no—
680C23—942no—
681C23—1884no—
682C23—1884no—
683C23—1884no—
684C23—1884no—
685C23C22×C4×D4712yes—
686C23#41×D4712yes—
687C23#41×D4712yes—
688C23#41×D4712yes—
689C23C2×#1062535412yes—
690C23#1309406912yes—
691C23#1309407012yes—
692C23C24×D4711yescharacteristic
693D4—9432no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—474no—
719C2×C4—474no—
720C2×C4—474no—
721C2×C4—948no—
722C2×C4—948no—
723C2×C4—948no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—18816no—
740C2×C4—18816no—
741C2×C4—18816no—
742C2×C4—18816no—
743C2×C4—1884no—
744C2×C4—1884no—
745C2×C4—1884no—
746C2×C4C22×C4×D4714yes—
747C2×C4C22×C4×D4714yes—
748C2×C4C22×C4×D4714yes—
749C2×C4C2×#1062535414yes—
750C22—478no—
751C22—9432no—
752C22—944no—
753C22—944no—
754C22—944no—
755C22—944no—
756C22—944no—
757C22—944no—
758C22—944no—
759C22—944no—
760C22—944no—
761C22—18816no—
762C22—1882no—
763C22—1882no—
764C22—1882no—
765C22—1882no—
766C22#117×D4714yes—
767C22C4×#1062535414yes—
768C22#1568959514yes—
769C22#1568979814yes—
770C22#1568980014yes—
771C22#1568981814yes—
772C22#1568982614yes—
773C22C23×C4×D4711yescharacteristic
774C22C2×#41×D4711yescharacteristic
775C22C2×#41×D4711yescharacteristic
776C22C2×#41×D4711yescharacteristic
777C22C22×#1062535411yescharacteristic
778C22C2×#1309406911yescharacteristic
779C22C2×#1309407011yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—24no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—944no—
788C4—944no—
789C4—944no—
790C4—1882no—
791C4—1882no—
792C4—1882no—
793C2—948no—
794C2—1884no—
795C2#2024632718yesdirect product factor
796C2C2×#117×D4711yescharacteristic
797C2C2×C4×#1062535411yescharacteristic
798C2C2×#1568959511yescharacteristic
799C2C2×#1568979811yescharacteristic
800C2C2×#1568980011yescharacteristic
801C2C2×#1568981811yescharacteristic
802C2C2×#1568982611yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#387C2
socleC24×C47C24
prime radicalC23×D188C22
cosocleC23×C47C25
hypercenterC2×#387D47
hypocenterC47C2×#2353
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#387

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20246327C2direct (N × H)
3. C2×#15689015C2semidirect
4. C2×#15689013C2semidirect
5. C2×#15689009C2semidirect
8. C2×#15688990C2semidirect
9. C2×#15688985C2semidirect
10. C2×#15688980C2semidirect
11. C2×C4×(C2×D47)⋊C4C2semidirect
12. C2×C4×(C2×D47)⋊C4C2semidirect
13. C2×#15688970C2semidirect
14. C2×#15688968C2semidirect
15. C2×#95×D47C2semidirect
16. C2×C47×#387C2semidirect
22. C2×#13093986C4semidirect
37. #15689015C22semidirect
38. #15689013C22semidirect
39. #15689009C22semidirect
42. #15688990C22semidirect
43. #15688985C22semidirect
44. #15688980C22semidirect
45. C4×(C2×D47)⋊C4C22semidirect
46. C4×(C2×D47)⋊C4C22semidirect
47. #15688970C22semidirect
48. #15688968C22semidirect
59. #95×D47C22semidirect
63. C47×#387C22semidirect
91. C22×C4×D47C2×C4semidirect
96. #13093986C2×C4semidirect
106. C2×(C2×D47)⋊C4C2×C4semidirect
118. C2×C4×Dic47C2×C4semidirect
141. C2×C4⋊C4×C47C2×C4semidirect
238. C2×C4×D47C22×C4semidirect
240. C4⋊C4×C47C22×C4semidirect
249. (C2×D47)⋊C4C22×C4semidirect
254. C4×Dic47C22×C4semidirect
397. C2×#387D47semidirect
408. C2×C47#2353semidirect
444. #387C2×D47semidirect
469. C47C2×#2353semidirect
509. C2×C4⋊C4C4×D47semidirect
643. C4⋊C4C2×C4×D47semidirect
795. C2#20246327direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#130939862
#202463272
C2×#156890152
C2×#156890132
C2×#156890092
C2×#156890012
C2×#156889902
C2×#156889852
C2×#156889802
C2×C4×(C2×D47)⋊C42
C2×#156889702
C2×#156889682
C2×#95×D472
C2×C47×#3872
C2×#235347